Beyond
the financial crisis: risk control and pricing methods
Satellite event of the 40th AIRO
meeting (September 8-11, 2009)
The 2007-2008 credit
crisis has witnessed an unprecedented deviation of market price dynamics from
long term fair values posing new challenges to financial practitioners and the
scientific community. The systemic extension of the crisis and the fall of
equity and bonds markets provides on the other hand an ideal stress event
to validate from a methodological viewpoint recent developments and new
theoretical assumptions. The aim of this workshop is to bring together practicioners and scientists to discuss and present
innovative approaches to deal with financial problems even in time of crisis.
14,30 – Leonardo Bellucci (MPS Capital services)
Beyond risk-neutral pricing, remaining fair (lesson from the crisis: the
right price, not the true one)
The explosive
innovation of derivative products has pushed quantitative finance away from its
roots, firmly grounded in market analysis and trading activities. During the
last decade, financial players have traded a vast range of exotic products,
priced with models which, despite their ever increasing complexity and
elegance, lack a solid foundation in the market mechanisms. The talk highlights
this phenomenon in the case of the volatility smile, showing how different
models produce very different results for exotic product prices and
plain-vanilla hedge ratios. We propose a research program which offers a
different (and in some ways more traditional) perspective on financial modeling,
formulating the valuation problem in terms more faithful to its original
meaning.
Leonardo Bellucci is currently Head of Staff Quants at MPS Capital Services. He obtained
a Ph.D. in Physics in 2002 at
15,00 – Alberto Bemporad (Università di
Siena)
Stochastic
receding horizon control for dynamic option hedging
Synthesizing
complex financial securities requires an underlying portfolio of simpler
securities that must be rebalanced dynamically to hedge the option writer
against risk. In this talk I will present a dynamic hedging approach based on
stochastic receding horizon control (also called stochastic model predictive
control) by converting an (approximate) option pricing engine into an hedging
engine that is applicable to a rather broad class of financial options. The
resulting stochastic optimization problem is simply solved at each trading date
as a least-squares problem with as many variables as the number of traded
assets and as many constraints as the number of predicted scenarios. The
approach is particularly useful and numerically viable for exotic options where
closed-form results are not available, and for relatively long expiration dates
where tree-based stochastic approaches are excessively complex.
Alberto Bemporad received the master degree in Electrical Engineering in
1993 and the Ph.D. in Control Engineering in 1997 from the University of
Florence, Italy. He spent the academic year 1996/97 at the Center for Robotics
and Automation, Dept. Systems Science & Mathematics, Washington University,
St. Louis, as a visiting researcher. In 1997-1999, he held a postdoctoral
position at the Automatic Control Lab, ETH, Zurich, Switzerland, where he
collaborated as a senior researcher in 2000-2002. Since 1999 he is with the
Faculty of Engineering of the University of Siena, Italy, where he is currently
an associate professor. He has published about 200 papers in the area of hybrid
systems, model predictive control, automotive control, multiparametric
optimization, computational geometry, and robotics. He is coauthor of the Model
Predictive Control Toolbox (The Mathworks, Inc.) and author of the Hybrid
Toolbox for Matlab. He was an Associate Editor of the
IEEE Transactions on Automatic Control during 2001-2004. He is Chair of the
Technical Committee on Hybrid Systems of the IEEE Control Systems Society since
2002.
15,30 – Tommaso Gabbriellini
(MPS Capital Services)
Inverse calibration method in derivatives pricing
Pricing an
illiquid derivative security can be seen as the problem of synthesizing that
security by means of a dynamic portfolio of liquid securities, which we refer
to as hedge instruments. Such a portfolio is known as a replication strategy,
and ultimately the price of the derivative security will be defined by the
least costly of these strategies. In order for a pricing model to correctly
determine a replication strategy, it must i)
faithfully capture the statistical properties of the risk sources, ii) be able
to reproduce the market prices of the hedge instruments, and iii) be compatible
with the traders’ viewpoint on the dynamic evolution of the market prices.
Calibrating a model in finance involves choosing its parameters in order to
achieve the best possibile trade-off between these
three objectives. In this presentation, after a brief introduction to basic
concepts in quantitative finance, I will illustrate some typical problems
that arise during the calibration of the Libor Market Model, the current
standard in interest rate derivatives modeling.
Tommaso Gabbriellini graduated in Physics at the University of
Florence and successively moved into the field of finance. He a took a master
degree in Quantitative Finance at Bocconi University
and immediately after started working at MPS Capital Services, his current
employer, as a quantitative analyst. He works on the development and
implementation of mathematical models for derivatives pricing.
16,00
- Coffee break
16,30
– Francesco Sandrini (Head of Institutional Investors
- Pioneers Investments)
2008 volatility regime and efficient portfolio management
We
propose to measure the value added by periodic portfolio rebalancing in
actively managed strategies. Using Monte Carlo simulation and dynamic
stochastic programming we simulate the pay off of an actively managed strategy.
We seek to replicate this pay-off using a static investment based on the same
Monte Carlo scenarios and investment timeframe, while including in the static portfolio
a set of derivative strategies not available to the active manager. We claim
that the allocation to the derivative strategies quantifies the value added by
an active management and test the solution sensitivity to various input
parameters. In particular we set the focus on understanding how the optimal
hedging strategy changes in different market volatility (and correlation)
regimes. We investigate data from the recent crisis and compare our solutions
over different past market regimes.
17
– Pierluigi Riva (CEO of Operational Research
Systems)
OR developments for efficient decision making in crisis periods
The credit crisis, the stock market downturn, and the
economic slowdown have pushed credit spreads to historic highs and caused
interest rates to fall sharply. This provides investors with extremely
interesting opportunities, but also poses serious challenges in terms of
optimal passive and active exposure to interest rate and credit risks.
Credit spreads are expected to narrow again but it is
highly uncertain when and how this will take place. Economic stimulus packages
will eventually result in increases in long term rates. Last but not
least, the fundamental scarcity of natural resources and political pressure on
central banks justify inflation fears for the medium to long term.
In these new market conditions, there is a clear and
pressing need for investors and asset managers to better understand the tools
that can be used to optimise investment in
fixed-income products and manage associated risks. A robust integrated software
environment for portfolio management and optimisation
can host applications building up on applied experience of this kind in a
natural and extendible fashion.
Pierluigi Riva
made his studies in Economics, Econometrics and Operational Research at the
University of Turin and at the London School of Economics. He has a long
experience in developing applications in Finance, Energy and Industrial
Environment. He is cofounder and president of Operational Research Systems, an Italian
company with over a decade experience in building enterprise software systems
based on the RAMS (Risk and Asset Management Studio) TM platform.
17,30 – Giorgio Consigli (Università di Bergamo)
- joint work with Gaetano Iaquinta (Università di Bergamo),
Patrizia Beraldi, Antonio Violi (Università della Calabria)
Simultaneous market and credit risk control on a generic corporate bond
portfolio during the credit crisis
We
present a multistage optimisation model that
integrates two correlated risk sources, market and credit risk, under very
general statistical assumptions and test the ability of the method to induce effective
risk control strategies during the crisis period. Specifically the two key
aspects of i) consistent risk factors statistical characterisation and ii) Effective dynamic optimization are
analysed jointly and implemented, from a numerical
viewpoint, in a scenario generator and a multistage stochastic programming
model to yield an integrated decision tool with practical relevance.
Giorgio Consigli is currently associate professor of applied
mathematics in economics and finance at the University of Bergamo and visiting
professor of finance at the University of Svizzera Italiana in Lugano. He has been
member of the Centre for Financial Research at the University of Cambridge
between 1995 and 1997 and Head of quant research at UniCredit
Banca Mobiliare, the
investment bank of the UniCredit banking group,
between 2000 and 2002. Since 2006 he is Director of FinMonitor
a privately funded research centre on financial institutions at the University
of Bergamo. In August 2007 he has been elected member of the International
Committee on Stochastic Programming (COSP). He has an active research
cooperation with the international academic and scientific world specifically
in the areas of stochastic optimization, financial modelling,
credit risk modelling and static and dynamic
portfolio selection. He has published with Cambridge University press,
North-Holland, Elsevier and several international Journals.
18
- Conclusions